import cudf
import cupy as cp
import plotly.graph_objects as go
import datashader as ds
import colorcet
import os
# Visualisation Imports
import numpy as np
import xarray as xr
# datashader
import datashader as ds
import datashader.transfer_functions as tf
from datashader.transfer_functions import shade
from datashader.transfer_functions import stack
from datashader.transfer_functions import dynspread
from datashader.transfer_functions import set_background
from datashader.transfer_functions import Images, Image
from datashader.colors import Elevation
from datashader.utils import orient_array
# holoviews
import holoviews as hv
from holoviews.plotting.plotly.dash import to_dash
from holoviews.element.tiles import CartoDark
from holoviews.operation.datashader import datashade, shade, dynspread, spread, rasterize
from holoviews.operation import decimate
# plotly
from plotly.colors import sequential
from plotly.subplots import make_subplots
# Dash Import
import dash
import dash_html_components as html
from jupyter_dash import JupyterDash
DATA_PATH = '../../data/hycom'
RES_PATH = '../../results/hycom'
df = cudf.read_csv(os.path.join(RES_PATH, 'hycom_equinox_merged-201920.csv'))
df.head()
| start_date | lat | lon | water_temp_0 | salinity_0 | water_temp_2 | salinity_2 | water_temp_4 | salinity_4 | water_temp_6 | ... | xCO2_ATM_interpolated_ppm | PRES_EQU_hPa | PRES_ATM@SSP_hPa | TEMP_EQU_C | SST_C | SAL_permil | fCO2_SW@SST_uatm | fCO2_ATM_interpolated_uatm | dfCO2_uatm | WOCE_QC_FLAG | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 2019-11-19 | 19.0418 | -87.4192 | 28.641375 | 36.191375 | 28.48175 | 36.194000 | 28.490375 | 36.193750 | 28.494625 | ... | 410.81 | 1014.72 | 1013.5662 | 29.14 | 29.1692 | 36.2848 | 410.02 | 393.66 | 16.36 | 2.0 |
| 1 | 2020-01-21 | 18.3305 | -65.1468 | 26.471600 | 35.826667 | 26.42980 | 35.825867 | 26.429333 | 35.828200 | 26.426533 | ... | 417.55 | 1015.40 | 1014.5055 | 27.25 | 27.3215 | 35.3726 | 390.25 | 402.13 | -11.88 | 2.0 |
| 2 | 2019-07-31 | 19.7638 | -87.1375 | 29.324125 | 36.082625 | 29.24825 | 36.083875 | 29.235125 | 36.083500 | 29.218875 | ... | 410.89 | 1014.90 | 1014.5565 | 29.98 | 29.7258 | 36.2400 | 435.94 | 393.63 | 42.32 | 2.0 |
| 3 | 2019-09-13 | 25.9173 | -79.9605 | 29.782625 | 36.122750 | 29.79925 | 36.123500 | 29.802750 | 36.124125 | 29.803750 | ... | 414.53 | 1012.47 | 1011.9442 | 29.88 | 29.9378 | 35.4666 | 413.24 | 395.84 | 17.40 | 2.0 |
| 4 | 2019-08-11 | 23.2150 | -83.5792 | 30.861500 | 36.154125 | 30.54200 | 36.152875 | 30.412500 | 36.150375 | 30.245500 | ... | 417.82 | 1017.40 | 1017.0594 | 30.57 | 30.6395 | 36.3900 | 442.06 | 400.40 | 41.66 | 2.0 |
5 rows × 26 columns
df = df[df['WOCE_QC_FLAG'] == 2]
df.head()
| start_date | lat | lon | water_temp_0 | salinity_0 | water_temp_2 | salinity_2 | water_temp_4 | salinity_4 | water_temp_6 | ... | xCO2_ATM_interpolated_ppm | PRES_EQU_hPa | PRES_ATM@SSP_hPa | TEMP_EQU_C | SST_C | SAL_permil | fCO2_SW@SST_uatm | fCO2_ATM_interpolated_uatm | dfCO2_uatm | WOCE_QC_FLAG | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 2019-11-19 | 19.0418 | -87.4192 | 28.641375 | 36.191375 | 28.48175 | 36.194000 | 28.490375 | 36.193750 | 28.494625 | ... | 410.81 | 1014.72 | 1013.5662 | 29.14 | 29.1692 | 36.2848 | 410.02 | 393.66 | 16.36 | 2.0 |
| 1 | 2020-01-21 | 18.3305 | -65.1468 | 26.471600 | 35.826667 | 26.42980 | 35.825867 | 26.429333 | 35.828200 | 26.426533 | ... | 417.55 | 1015.40 | 1014.5055 | 27.25 | 27.3215 | 35.3726 | 390.25 | 402.13 | -11.88 | 2.0 |
| 2 | 2019-07-31 | 19.7638 | -87.1375 | 29.324125 | 36.082625 | 29.24825 | 36.083875 | 29.235125 | 36.083500 | 29.218875 | ... | 410.89 | 1014.90 | 1014.5565 | 29.98 | 29.7258 | 36.2400 | 435.94 | 393.63 | 42.32 | 2.0 |
| 3 | 2019-09-13 | 25.9173 | -79.9605 | 29.782625 | 36.122750 | 29.79925 | 36.123500 | 29.802750 | 36.124125 | 29.803750 | ... | 414.53 | 1012.47 | 1011.9442 | 29.88 | 29.9378 | 35.4666 | 413.24 | 395.84 | 17.40 | 2.0 |
| 4 | 2019-08-11 | 23.2150 | -83.5792 | 30.861500 | 36.154125 | 30.54200 | 36.152875 | 30.412500 | 36.150375 | 30.245500 | ... | 417.82 | 1017.40 | 1017.0594 | 30.57 | 30.6395 | 36.3900 | 442.06 | 400.40 | 41.66 | 2.0 |
5 rows × 26 columns
Dropping date, lat and lon since these are not expected to significantly impact relationships
df.drop(['start_date', 'lat', 'lon', 'WOCE_QC_FLAG', 'easting', 'northing'], axis=1, inplace=True)
df.head()
| water_temp_0 | salinity_0 | water_temp_2 | salinity_2 | water_temp_4 | salinity_4 | water_temp_6 | salinity_6 | water_temp_8 | salinity_8 | xCO2_EQU_ppm | xCO2_ATM_interpolated_ppm | PRES_EQU_hPa | PRES_ATM@SSP_hPa | TEMP_EQU_C | SST_C | SAL_permil | fCO2_SW@SST_uatm | fCO2_ATM_interpolated_uatm | dfCO2_uatm | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 28.641375 | 36.191375 | 28.48175 | 36.194000 | 28.490375 | 36.193750 | 28.494625 | 36.193500 | 28.495625 | 36.193250 | 426.816 | 410.81 | 1014.72 | 1013.5662 | 29.14 | 29.1692 | 36.2848 | 410.02 | 393.66 | 16.36 |
| 1 | 26.471600 | 35.826667 | 26.42980 | 35.825867 | 26.429333 | 35.828200 | 26.426533 | 35.830333 | 26.422667 | 35.832533 | 403.554 | 417.55 | 1015.40 | 1014.5055 | 27.25 | 27.3215 | 35.3726 | 390.25 | 402.13 | -11.88 |
| 2 | 29.324125 | 36.082625 | 29.24825 | 36.083875 | 29.235125 | 36.083500 | 29.218875 | 36.083000 | 29.198750 | 36.082250 | 460.100 | 410.89 | 1014.90 | 1014.5565 | 29.98 | 29.7258 | 36.2400 | 435.94 | 393.63 | 42.32 |
| 3 | 29.782625 | 36.122750 | 29.79925 | 36.123500 | 29.802750 | 36.124125 | 29.803750 | 36.124375 | 29.803375 | 36.124375 | 431.397 | 414.53 | 1012.47 | 1011.9442 | 29.88 | 29.9378 | 35.4666 | 413.24 | 395.84 | 17.40 |
| 4 | 30.861500 | 36.154125 | 30.54200 | 36.152875 | 30.412500 | 36.150375 | 30.245500 | 36.148625 | 29.899750 | 36.150000 | 459.698 | 417.82 | 1017.40 | 1017.0594 | 30.57 | 30.6395 | 36.3900 | 442.06 | 400.40 | 41.66 |
from statsmodels.regression import linear_model
import pandas as pd
from sklearn.preprocessing import PolynomialFeatures
X_col_names = ['water_temp_0', 'salinity_0', 'water_temp_2', 'salinity_2', 'water_temp_4', 'salinity_4', 'water_temp_6', 'salinity_6', 'water_temp_8', 'salinity_8']
def fit_model(df, pred_col):
X = df[X_col_names]
y = df[[col]]
model = linear_model.OLS(y, X).fit()
print(model_summary)
def fit_interaction_model(df, pred_col):
df = df.dropna()
X = df[X_col_names]
y = df[[pred_col]]
poly_features = PolynomialFeatures(2, interaction_only=True, include_bias=False)
X_inter = poly_features.fit_transform(X.as_gpu_matrix())
X_df = cudf.DataFrame(X_inter, columns=poly_features.get_feature_names(X.columns))
inter_model = linear_model.OLS(y.to_pandas().values, X_df.to_pandas()).fit()
# inter_model = inter_model.pvalues[inter_model.pvalues < 0.05]
print(inter_model.summary())
df = df.dropna()
X = df[X_col_names]
equinox_col_names = dict({
'xCO2_EQU_ppm': 'Mole fraction of CO2 in the equilibrator headspace (ppm)',
'xCO2_ATM_interpolated_ppm': 'Mole fraction of CO2 measured in dry outside air (ppm)',
'PRES_EQU_hPa': 'Barometric pressure in the equilibrator headspace (hPa)',
'PRES_ATM@SSP_hPa': 'Barometric pressure measured outside, corrected to sea level (hPa)',
'TEMP_EQU_C': 'Water temperature in equilibrator (°C)',
'SST_C': 'Sea surface temperature (°C)',
'SAL_permil': 'Sea surface salinity on Practical Salinity Scale (ppt)',
'fCO2_SW@SST_uatm': 'Fugacity of CO2 in sea water at SST and 100% humidity (μatm)',
'fCO2_ATM_interpolated_uatm': 'Fugacity of CO2 in air corresponding to the interpolated xCO2 at SST and 100% humidity (μatm)',
'dfCO2_uatm': 'Sea water fCO2 minus interpolated air fCO2 (μatm)' ,
})
poly_features = PolynomialFeatures(2, interaction_only=True, include_bias=False)
X_inter = poly_features.fit_transform(X.as_gpu_matrix())
X_inter_cols = poly_features.get_feature_names(X.columns)
X_df = cudf.DataFrame(X_inter, columns=poly_features.get_feature_names(X.columns))
def plot_correlation(df, hycom_col):
graph_list = []
data = pd.concat([X_df.to_pandas(), df[hycom_col].to_pandas()], axis=1)
hv_data = hv.Dataset(data)
for idx, col in enumerate(X_inter_cols):
scatter = hv.Scatter(hv_data, kdims=col, vdims=hycom_col).opts(width=600, height=400, title=equinox_col_names[hycom_col])
scatter.redim(y=hv.Dimension(col))
shaded = decimate(scatter, y_range=(0, data[hycom_col].max())).opts(width=600, height=400)
graph_list.append(shaded)
del scatter
layout = hv.Layout(graph_list).cols(2)
return layout
plot_correlation(df, 'xCO2_EQU_ppm')
plot_correlation(df, 'xCO2_ATM_interpolated_ppm')
plot_correlation(df, 'fCO2_SW@SST_uatm')
plot_correlation(df, 'fCO2_ATM_interpolated_uatm')
plot_correlation(df, 'dfCO2_uatm')
fit_interaction_model(df, 'xCO2_ATM_interpolated_ppm')
OLS Regression Results
=======================================================================================
Dep. Variable: y R-squared (uncentered): 0.566
Model: OLS Adj. R-squared (uncentered): 0.565
Method: Least Squares F-statistic: 2694.
Date: Tue, 15 Jun 2021 Prob (F-statistic): 0.00
Time: 19:56:38 Log-Likelihood: -8.1238e+05
No. Observations: 113837 AIC: 1.625e+06
Df Residuals: 113782 BIC: 1.625e+06
Df Model: 55
Covariance Type: nonrobust
=============================================================================================
coef std err t P>|t| [0.025 0.975]
---------------------------------------------------------------------------------------------
water_temp_0 2117.2401 2485.582 0.852 0.394 -2754.463 6988.943
salinity_0 -6.688e+04 6.74e+04 -0.993 0.321 -1.99e+05 6.52e+04
water_temp_2 -5327.7334 1.03e+04 -0.518 0.605 -2.55e+04 1.48e+04
salinity_2 9.175e+04 1.56e+05 0.588 0.557 -2.14e+05 3.98e+05
water_temp_4 -1.936e+04 2.6e+04 -0.743 0.457 -7.04e+04 3.17e+04
salinity_4 -8813.0707 2.59e+05 -0.034 0.973 -5.17e+05 5e+05
water_temp_6 3.594e+04 2.67e+04 1.347 0.178 -1.63e+04 8.82e+04
salinity_6 -4.096e+04 2.2e+05 -0.186 0.853 -4.73e+05 3.91e+05
water_temp_8 -1.343e+04 1e+04 -1.341 0.180 -3.31e+04 6205.813
salinity_8 2.495e+04 6.03e+04 0.413 0.679 -9.33e+04 1.43e+05
water_temp_0 salinity_0 1631.3642 5834.485 0.280 0.780 -9804.137 1.31e+04
water_temp_0 water_temp_2 633.3594 369.572 1.714 0.087 -90.995 1357.714
water_temp_0 salinity_2 -1.687e+04 1.18e+04 -1.434 0.152 -3.99e+04 6187.248
water_temp_0 water_temp_4 -1601.6124 1638.801 -0.977 0.328 -4813.637 1610.412
water_temp_0 salinity_4 2795.3105 2.71e+04 0.103 0.918 -5.04e+04 5.6e+04
water_temp_0 water_temp_6 365.1563 2177.643 0.168 0.867 -3902.990 4633.303
water_temp_0 salinity_6 2.233e+04 2.43e+04 0.918 0.359 -2.54e+04 7e+04
water_temp_0 water_temp_8 668.6167 879.669 0.760 0.447 -1055.520 2392.754
water_temp_0 salinity_8 -1e+04 5806.418 -1.722 0.085 -2.14e+04 1378.965
salinity_0 water_temp_2 -1.865e+04 3.01e+04 -0.619 0.536 -7.77e+04 4.04e+04
salinity_0 salinity_2 -2.888e+04 3.43e+04 -0.843 0.399 -9.6e+04 3.83e+04
salinity_0 water_temp_4 1.9e+05 9.37e+04 2.028 0.043 6402.860 3.74e+05
salinity_0 salinity_4 4.244e+05 3.42e+05 1.241 0.214 -2.46e+05 1.09e+06
salinity_0 water_temp_6 -2.665e+05 9.8e+04 -2.719 0.007 -4.59e+05 -7.44e+04
salinity_0 salinity_6 -4.205e+05 4.1e+05 -1.025 0.306 -1.22e+06 3.84e+05
salinity_0 water_temp_8 9.418e+04 3.45e+04 2.732 0.006 2.66e+04 1.62e+05
salinity_0 salinity_8 2.631e+04 1.29e+05 0.204 0.838 -2.26e+05 2.79e+05
water_temp_2 salinity_2 5.94e+04 5.45e+04 1.091 0.275 -4.73e+04 1.66e+05
water_temp_2 water_temp_4 -1638.5309 1641.885 -0.998 0.318 -4856.600 1579.538
water_temp_2 salinity_4 -1.243e+05 8.48e+04 -1.466 0.143 -2.9e+05 4.19e+04
water_temp_2 water_temp_6 5115.3098 3497.749 1.462 0.144 -1740.226 1.2e+04
water_temp_2 salinity_6 7.401e+04 7.33e+04 1.010 0.312 -6.96e+04 2.18e+05
water_temp_2 water_temp_8 -4374.1540 2065.173 -2.118 0.034 -8421.862 -326.446
water_temp_2 salinity_8 9884.7059 1.72e+04 0.573 0.566 -2.39e+04 4.37e+04
salinity_2 water_temp_4 -4.011e+05 1.72e+05 -2.328 0.020 -7.39e+05 -6.34e+04
salinity_2 salinity_4 -4.525e+05 3.37e+05 -1.343 0.179 -1.11e+06 2.08e+05
salinity_2 water_temp_6 5.628e+05 1.87e+05 3.008 0.003 1.96e+05 9.29e+05
salinity_2 salinity_6 6.468e+05 5.1e+05 1.268 0.205 -3.53e+05 1.65e+06
salinity_2 water_temp_8 -2.053e+05 6.94e+04 -2.960 0.003 -3.41e+05 -6.94e+04
salinity_2 salinity_8 -1.67e+05 2.03e+05 -0.823 0.411 -5.65e+05 2.31e+05
water_temp_4 salinity_4 5.431e+05 2.23e+05 2.437 0.015 1.06e+05 9.8e+05
water_temp_4 water_temp_6 -2998.6293 1484.430 -2.020 0.043 -5908.090 -89.169
water_temp_4 salinity_6 -3.773e+05 1.7e+05 -2.218 0.027 -7.11e+05 -4.38e+04
water_temp_4 water_temp_8 6882.3059 2350.781 2.928 0.003 2274.812 1.15e+04
water_temp_4 salinity_8 4.534e+04 4e+04 1.133 0.257 -3.31e+04 1.24e+05
salinity_4 water_temp_6 -5.898e+05 2.33e+05 -2.533 0.011 -1.05e+06 -1.33e+05
salinity_4 salinity_6 -1.693e+05 1.22e+05 -1.390 0.164 -4.08e+05 6.93e+04
salinity_4 water_temp_8 1.684e+05 8.73e+04 1.931 0.054 -2572.577 3.39e+05
salinity_4 salinity_8 1.973e+05 1.4e+05 1.410 0.158 -7.69e+04 4.71e+05
water_temp_6 salinity_6 3.567e+05 1.61e+05 2.214 0.027 4.1e+04 6.73e+05
water_temp_6 water_temp_8 -3051.0309 881.856 -3.460 0.001 -4779.454 -1322.607
water_temp_6 salinity_8 -6.378e+04 3.33e+04 -1.915 0.056 -1.29e+05 1510.171
salinity_6 water_temp_8 -7.484e+04 5.8e+04 -1.291 0.197 -1.88e+05 3.88e+04
salinity_6 salinity_8 -5.672e+04 5.34e+04 -1.063 0.288 -1.61e+05 4.79e+04
water_temp_8 salinity_8 1.782e+04 9849.164 1.810 0.070 -1481.644 3.71e+04
==============================================================================
Omnibus: 93819.299 Durbin-Watson: 1.999
Prob(Omnibus): 0.000 Jarque-Bera (JB): 1479030.029
Skew: -4.183 Prob(JB): 0.00
Kurtosis: 18.550 Cond. No. 6.36e+09
==============================================================================
Notes:
[1] R² is computed without centering (uncentered) since the model does not contain a constant.
[2] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[3] The condition number is large, 6.36e+09. This might indicate that there are
strong multicollinearity or other numerical problems.
# equinox_cols = ['xCO2_EQU_ppm',
# 'xCO2_ATM_interpolated_ppm',
# 'PRES_EQU_hPa',
# 'PRES_ATM@SSP_hPa',
# 'TEMP_EQU_C',
# 'SST_C',
# 'SAL_permil',
# 'fCO2_SW@SST_uatm',
# 'fCO2_ATM_interpolated_uatm',
# 'dfCO2_uatm']
fit_interaction_model(df, 'xCO2_ATM_interpolated_ppm')
fit_interaction_model(df, 'PRES_EQU_hPa')
OLS Regression Results
=======================================================================================
Dep. Variable: y R-squared (uncentered): 0.818
Model: OLS Adj. R-squared (uncentered): 0.818
Method: Least Squares F-statistic: 9305.
Date: Tue, 15 Jun 2021 Prob (F-statistic): 0.00
Time: 19:58:25 Log-Likelihood: -8.5273e+05
No. Observations: 113837 AIC: 1.706e+06
Df Residuals: 113782 BIC: 1.706e+06
Df Model: 55
Covariance Type: nonrobust
=============================================================================================
coef std err t P>|t| [0.025 0.975]
---------------------------------------------------------------------------------------------
water_temp_0 3027.9221 3542.791 0.855 0.393 -3915.895 9971.740
salinity_0 -8.197e+04 9.6e+04 -0.854 0.393 -2.7e+05 1.06e+05
water_temp_2 -1.161e+04 1.47e+04 -0.792 0.428 -4.04e+04 1.71e+04
salinity_2 1.667e+05 2.22e+05 0.749 0.454 -2.69e+05 6.03e+05
water_temp_4 -1.132e+04 3.71e+04 -0.305 0.760 -8.41e+04 6.14e+04
salinity_4 -8.042e+04 3.7e+05 -0.218 0.828 -8.05e+05 6.44e+05
water_temp_6 3.353e+04 3.8e+04 0.882 0.378 -4.1e+04 1.08e+05
salinity_6 -4.579e+04 3.14e+05 -0.146 0.884 -6.61e+05 5.7e+05
water_temp_8 -1.363e+04 1.43e+04 -0.955 0.340 -4.16e+04 1.44e+04
salinity_8 4.154e+04 8.6e+04 0.483 0.629 -1.27e+05 2.1e+05
water_temp_0 salinity_0 2546.0588 8316.105 0.306 0.759 -1.38e+04 1.88e+04
water_temp_0 water_temp_2 844.8312 526.764 1.604 0.109 -187.618 1877.280
water_temp_0 salinity_2 -2.347e+04 1.68e+04 -1.400 0.162 -5.63e+04 9392.139
water_temp_0 water_temp_4 -1337.6896 2335.843 -0.573 0.567 -5915.906 3240.527
water_temp_0 salinity_4 7510.5214 3.87e+04 0.194 0.846 -6.83e+04 8.33e+04
water_temp_0 water_temp_6 -852.0921 3103.874 -0.275 0.784 -6935.638 5231.454
water_temp_0 salinity_6 2.702e+04 3.47e+04 0.779 0.436 -4.1e+04 9.5e+04
water_temp_0 water_temp_8 1440.8890 1253.824 1.149 0.250 -1016.587 3898.365
water_temp_0 salinity_8 -1.377e+04 8276.101 -1.664 0.096 -3e+04 2450.110
salinity_0 water_temp_2 -2.671e+04 4.29e+04 -0.622 0.534 -1.11e+05 5.75e+04
salinity_0 salinity_2 -3.323e+04 4.88e+04 -0.681 0.496 -1.29e+05 6.25e+04
salinity_0 water_temp_4 2.779e+05 1.34e+05 2.082 0.037 1.62e+04 5.4e+05
salinity_0 salinity_4 5.907e+05 4.87e+05 1.212 0.225 -3.64e+05 1.55e+06
salinity_0 water_temp_6 -4.005e+05 1.4e+05 -2.867 0.004 -6.74e+05 -1.27e+05
salinity_0 salinity_6 -6.186e+05 5.85e+05 -1.058 0.290 -1.77e+06 5.28e+05
salinity_0 water_temp_8 1.474e+05 4.91e+04 3.001 0.003 5.11e+04 2.44e+05
salinity_0 salinity_8 6.292e+04 1.84e+05 0.342 0.732 -2.97e+05 4.23e+05
water_temp_2 salinity_2 8.064e+04 7.76e+04 1.039 0.299 -7.15e+04 2.33e+05
water_temp_2 water_temp_4 -3028.1460 2340.238 -1.294 0.196 -7614.978 1558.686
water_temp_2 salinity_4 -1.784e+05 1.21e+05 -1.476 0.140 -4.15e+05 5.85e+04
water_temp_2 water_temp_6 8916.7328 4985.471 1.789 0.074 -854.714 1.87e+04
water_temp_2 salinity_6 1.148e+05 1.04e+05 1.099 0.272 -8.99e+04 3.19e+05
water_temp_2 water_temp_8 -7104.1989 2943.567 -2.413 0.016 -1.29e+04 -1334.852
water_temp_2 salinity_8 1.026e+04 2.46e+04 0.417 0.676 -3.79e+04 5.84e+04
salinity_2 water_temp_4 -5.768e+05 2.46e+05 -2.348 0.019 -1.06e+06 -9.54e+04
salinity_2 salinity_4 -6.321e+05 4.8e+05 -1.317 0.188 -1.57e+06 3.09e+05
salinity_2 water_temp_6 8.323e+05 2.67e+05 3.121 0.002 3.1e+05 1.36e+06
salinity_2 salinity_6 9.227e+05 7.27e+05 1.269 0.204 -5.02e+05 2.35e+06
salinity_2 water_temp_8 -3.145e+05 9.89e+04 -3.181 0.001 -5.08e+05 -1.21e+05
salinity_2 salinity_8 -2.605e+05 2.89e+05 -0.901 0.368 -8.27e+05 3.06e+05
water_temp_4 salinity_4 7.612e+05 3.18e+05 2.396 0.017 1.39e+05 1.38e+06
water_temp_4 water_temp_6 -4671.1997 2115.813 -2.208 0.027 -8818.161 -524.239
water_temp_4 salinity_6 -5.343e+05 2.42e+05 -2.204 0.028 -1.01e+06 -5.91e+04
water_temp_4 water_temp_8 9864.9775 3350.654 2.944 0.003 3297.746 1.64e+04
water_temp_4 salinity_8 7.166e+04 5.7e+04 1.257 0.209 -4.01e+04 1.83e+05
salinity_4 water_temp_6 -8.314e+05 3.32e+05 -2.505 0.012 -1.48e+06 -1.81e+05
salinity_4 salinity_6 -2.293e+05 1.74e+05 -1.322 0.186 -5.69e+05 1.11e+05
salinity_4 water_temp_8 2.411e+05 1.24e+05 1.939 0.053 -2658.627 4.85e+05
salinity_4 salinity_8 2.728e+05 1.99e+05 1.368 0.171 -1.18e+05 6.64e+05
water_temp_6 salinity_6 4.938e+05 2.3e+05 2.150 0.032 4.37e+04 9.44e+05
water_temp_6 water_temp_8 -4073.9961 1256.941 -3.241 0.001 -6537.582 -1610.411
water_temp_6 salinity_8 -9.468e+04 4.75e+04 -1.994 0.046 -1.88e+05 -1618.197
salinity_6 water_temp_8 -9.907e+04 8.26e+04 -1.199 0.230 -2.61e+05 6.29e+04
salinity_6 salinity_8 -7.531e+04 7.61e+04 -0.990 0.322 -2.24e+05 7.38e+04
water_temp_8 salinity_8 2.53e+04 1.4e+04 1.803 0.071 -2210.439 5.28e+04
==============================================================================
Omnibus: 93891.307 Durbin-Watson: 1.999
Prob(Omnibus): 0.000 Jarque-Bera (JB): 1481982.320
Skew: -4.188 Prob(JB): 0.00
Kurtosis: 18.566 Cond. No. 6.36e+09
==============================================================================
Notes:
[1] R² is computed without centering (uncentered) since the model does not contain a constant.
[2] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[3] The condition number is large, 6.36e+09. This might indicate that there are
strong multicollinearity or other numerical problems.
fit_interaction_model(df, 'PRES_ATM@SSP_hPa')
OLS Regression Results
=======================================================================================
Dep. Variable: y R-squared (uncentered): 0.818
Model: OLS Adj. R-squared (uncentered): 0.818
Method: Least Squares F-statistic: 9295.
Date: Tue, 15 Jun 2021 Prob (F-statistic): 0.00
Time: 19:58:26 Log-Likelihood: -8.5267e+05
No. Observations: 113837 AIC: 1.705e+06
Df Residuals: 113782 BIC: 1.706e+06
Df Model: 55
Covariance Type: nonrobust
=============================================================================================
coef std err t P>|t| [0.025 0.975]
---------------------------------------------------------------------------------------------
water_temp_0 3005.9790 3541.034 0.849 0.396 -3934.393 9946.351
salinity_0 -8.267e+04 9.6e+04 -0.861 0.389 -2.71e+05 1.05e+05
water_temp_2 -1.147e+04 1.47e+04 -0.782 0.434 -4.02e+04 1.73e+04
salinity_2 1.663e+05 2.22e+05 0.748 0.455 -2.7e+05 6.02e+05
water_temp_4 -1.186e+04 3.71e+04 -0.320 0.749 -8.46e+04 6.08e+04
salinity_4 -8.017e+04 3.7e+05 -0.217 0.828 -8.04e+05 6.44e+05
water_temp_6 3.371e+04 3.8e+04 0.887 0.375 -4.08e+04 1.08e+05
salinity_6 -4.437e+04 3.14e+05 -0.141 0.888 -6.6e+05 5.71e+05
water_temp_8 -1.338e+04 1.43e+04 -0.937 0.349 -4.14e+04 1.46e+04
salinity_8 4.098e+04 8.6e+04 0.477 0.634 -1.28e+05 2.09e+05
water_temp_0 salinity_0 2682.9987 8311.979 0.323 0.747 -1.36e+04 1.9e+04
water_temp_0 water_temp_2 836.3581 526.503 1.589 0.112 -195.579 1868.295
water_temp_0 salinity_2 -2.367e+04 1.68e+04 -1.413 0.158 -5.65e+04 9173.286
water_temp_0 water_temp_4 -1316.7359 2334.684 -0.564 0.573 -5892.681 3259.209
water_temp_0 salinity_4 7424.8887 3.86e+04 0.192 0.848 -6.83e+04 8.32e+04
water_temp_0 water_temp_6 -872.6940 3102.334 -0.281 0.778 -6953.222 5207.834
water_temp_0 salinity_6 2.716e+04 3.47e+04 0.784 0.433 -4.08e+04 9.51e+04
water_temp_0 water_temp_8 1448.9436 1253.202 1.156 0.248 -1007.313 3905.200
water_temp_0 salinity_8 -1.376e+04 8271.995 -1.664 0.096 -3e+04 2452.102
salinity_0 water_temp_2 -2.772e+04 4.29e+04 -0.646 0.518 -1.12e+05 5.64e+04
salinity_0 salinity_2 -3.364e+04 4.88e+04 -0.689 0.491 -1.29e+05 6.2e+04
salinity_0 water_temp_4 2.812e+05 1.33e+05 2.107 0.035 1.97e+04 5.43e+05
salinity_0 salinity_4 5.924e+05 4.87e+05 1.216 0.224 -3.62e+05 1.55e+06
salinity_0 water_temp_6 -4.035e+05 1.4e+05 -2.891 0.004 -6.77e+05 -1.3e+05
salinity_0 salinity_6 -6.201e+05 5.85e+05 -1.061 0.289 -1.77e+06 5.26e+05
salinity_0 water_temp_8 1.481e+05 4.91e+04 3.015 0.003 5.18e+04 2.44e+05
salinity_0 salinity_8 6.314e+04 1.84e+05 0.344 0.731 -2.97e+05 4.23e+05
water_temp_2 salinity_2 8.223e+04 7.76e+04 1.060 0.289 -6.98e+04 2.34e+05
water_temp_2 water_temp_4 -3021.3994 2339.077 -1.292 0.196 -7605.956 1563.157
water_temp_2 salinity_4 -1.78e+05 1.21e+05 -1.474 0.140 -4.15e+05 5.87e+04
water_temp_2 water_temp_6 8913.3252 4982.997 1.789 0.074 -853.274 1.87e+04
water_temp_2 salinity_6 1.138e+05 1.04e+05 1.090 0.276 -9.08e+04 3.18e+05
water_temp_2 water_temp_8 -7099.9697 2942.107 -2.413 0.016 -1.29e+04 -1333.485
water_temp_2 salinity_8 1.034e+04 2.46e+04 0.421 0.674 -3.78e+04 5.85e+04
salinity_2 water_temp_4 -5.823e+05 2.45e+05 -2.372 0.018 -1.06e+06 -1.01e+05
salinity_2 salinity_4 -6.348e+05 4.8e+05 -1.323 0.186 -1.58e+06 3.06e+05
salinity_2 water_temp_6 8.377e+05 2.67e+05 3.143 0.002 3.15e+05 1.36e+06
salinity_2 salinity_6 9.276e+05 7.27e+05 1.277 0.202 -4.97e+05 2.35e+06
salinity_2 water_temp_8 -3.156e+05 9.88e+04 -3.194 0.001 -5.09e+05 -1.22e+05
salinity_2 salinity_8 -2.623e+05 2.89e+05 -0.907 0.364 -8.29e+05 3.04e+05
water_temp_4 salinity_4 7.623e+05 3.18e+05 2.401 0.016 1.4e+05 1.38e+06
water_temp_4 water_temp_6 -4666.2528 2114.763 -2.207 0.027 -8811.156 -521.349
water_temp_4 salinity_6 -5.328e+05 2.42e+05 -2.199 0.028 -1.01e+06 -5.78e+04
water_temp_4 water_temp_8 9841.5523 3348.992 2.939 0.003 3277.580 1.64e+04
water_temp_4 salinity_8 7.137e+04 5.7e+04 1.252 0.210 -4.03e+04 1.83e+05
salinity_4 water_temp_6 -8.331e+05 3.32e+05 -2.512 0.012 -1.48e+06 -1.83e+05
salinity_4 salinity_6 -2.313e+05 1.73e+05 -1.334 0.182 -5.71e+05 1.09e+05
salinity_4 water_temp_8 2.416e+05 1.24e+05 1.944 0.052 -2044.246 4.85e+05
salinity_4 salinity_8 2.757e+05 1.99e+05 1.383 0.167 -1.15e+05 6.66e+05
water_temp_6 salinity_6 4.931e+05 2.3e+05 2.148 0.032 4.32e+04 9.43e+05
water_temp_6 water_temp_8 -4063.0526 1256.317 -3.234 0.001 -6525.416 -1600.689
water_temp_6 salinity_8 -9.454e+04 4.75e+04 -1.992 0.046 -1.88e+05 -1520.310
salinity_6 water_temp_8 -9.915e+04 8.26e+04 -1.201 0.230 -2.61e+05 6.27e+04
salinity_6 salinity_8 -7.672e+04 7.6e+04 -1.009 0.313 -2.26e+05 7.23e+04
water_temp_8 salinity_8 2.538e+04 1.4e+04 1.809 0.070 -2120.526 5.29e+04
==============================================================================
Omnibus: 93891.855 Durbin-Watson: 1.999
Prob(Omnibus): 0.000 Jarque-Bera (JB): 1482011.308
Skew: -4.188 Prob(JB): 0.00
Kurtosis: 18.566 Cond. No. 6.36e+09
==============================================================================
Notes:
[1] R² is computed without centering (uncentered) since the model does not contain a constant.
[2] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[3] The condition number is large, 6.36e+09. This might indicate that there are
strong multicollinearity or other numerical problems.
fit_interaction_model(df, 'TEMP_EQU_C')
OLS Regression Results
=======================================================================================
Dep. Variable: y R-squared (uncentered): 0.011
Model: OLS Adj. R-squared (uncentered): 0.011
Method: Least Squares F-statistic: 23.59
Date: Tue, 15 Jun 2021 Prob (F-statistic): 1.00e-233
Time: 19:58:28 Log-Likelihood: -7.7592e+05
No. Observations: 113837 AIC: 1.552e+06
Df Residuals: 113782 BIC: 1.552e+06
Df Model: 55
Covariance Type: nonrobust
=============================================================================================
coef std err t P>|t| [0.025 0.975]
---------------------------------------------------------------------------------------------
water_temp_0 1397.3877 1804.251 0.774 0.439 -2138.916 4933.692
salinity_0 -4.485e+04 4.89e+04 -0.917 0.359 -1.41e+05 5.1e+04
water_temp_2 -5294.4108 7467.864 -0.709 0.478 -1.99e+04 9342.490
salinity_2 8.486e+04 1.13e+05 0.749 0.454 -1.37e+05 3.07e+05
water_temp_4 -6947.5498 1.89e+04 -0.368 0.713 -4.4e+04 3.01e+04
salinity_4 -3.07e+04 1.88e+05 -0.163 0.870 -4e+05 3.38e+05
water_temp_6 1.866e+04 1.94e+04 0.964 0.335 -1.93e+04 5.66e+04
salinity_6 -2.94e+04 1.6e+05 -0.184 0.854 -3.43e+05 2.84e+05
water_temp_8 -7804.7857 7273.118 -1.073 0.283 -2.21e+04 6450.416
salinity_8 2.007e+04 4.38e+04 0.458 0.647 -6.58e+04 1.06e+05
water_temp_0 salinity_0 1570.5106 4235.174 0.371 0.711 -6730.366 9871.388
water_temp_0 water_temp_2 401.0032 268.267 1.495 0.135 -124.796 926.803
water_temp_0 salinity_2 -1.195e+04 8537.676 -1.400 0.162 -2.87e+04 4783.172
water_temp_0 water_temp_4 -650.9287 1189.583 -0.547 0.584 -2982.494 1680.637
water_temp_0 salinity_4 2941.0882 1.97e+04 0.149 0.881 -3.57e+04 4.15e+04
water_temp_0 water_temp_6 -414.8093 1580.722 -0.262 0.793 -3513.000 2683.381
water_temp_0 salinity_6 1.452e+04 1.77e+04 0.822 0.411 -2.01e+04 4.91e+04
water_temp_0 water_temp_8 713.1715 638.540 1.117 0.264 -538.356 1964.700
water_temp_0 salinity_8 -7157.0100 4214.801 -1.698 0.089 -1.54e+04 1103.936
salinity_0 water_temp_2 -1.479e+04 2.19e+04 -0.676 0.499 -5.77e+04 2.81e+04
salinity_0 salinity_2 -1.702e+04 2.49e+04 -0.684 0.494 -6.58e+04 3.17e+04
salinity_0 water_temp_4 1.419e+05 6.8e+04 2.086 0.037 8598.585 2.75e+05
salinity_0 salinity_4 2.928e+05 2.48e+05 1.180 0.238 -1.94e+05 7.79e+05
salinity_0 water_temp_6 -2.03e+05 7.11e+04 -2.854 0.004 -3.42e+05 -6.36e+04
salinity_0 salinity_6 -3.057e+05 2.98e+05 -1.026 0.305 -8.89e+05 2.78e+05
salinity_0 water_temp_8 7.474e+04 2.5e+04 2.987 0.003 2.57e+04 1.24e+05
salinity_0 salinity_8 3.077e+04 9.36e+04 0.329 0.742 -1.53e+05 2.14e+05
water_temp_2 salinity_2 4.413e+04 3.95e+04 1.116 0.264 -3.33e+04 1.22e+05
water_temp_2 water_temp_4 -1479.7946 1191.822 -1.242 0.214 -3815.748 856.158
water_temp_2 salinity_4 -9.226e+04 6.15e+04 -1.499 0.134 -2.13e+05 2.84e+04
water_temp_2 water_temp_6 4411.5002 2538.969 1.738 0.082 -564.841 9387.842
water_temp_2 salinity_6 5.734e+04 5.32e+04 1.078 0.281 -4.69e+04 1.62e+05
water_temp_2 water_temp_8 -3521.3203 1499.082 -2.349 0.019 -6459.497 -583.143
water_temp_2 salinity_8 5863.2156 1.25e+04 0.469 0.639 -1.87e+04 3.04e+04
salinity_2 water_temp_4 -2.978e+05 1.25e+05 -2.381 0.017 -5.43e+05 -5.27e+04
salinity_2 salinity_4 -3.135e+05 2.44e+05 -1.282 0.200 -7.93e+05 1.66e+05
salinity_2 water_temp_6 4.24e+05 1.36e+05 3.122 0.002 1.58e+05 6.9e+05
salinity_2 salinity_6 4.604e+05 3.7e+05 1.244 0.214 -2.65e+05 1.19e+06
salinity_2 water_temp_8 -1.593e+05 5.04e+04 -3.163 0.002 -2.58e+05 -6.06e+04
salinity_2 salinity_8 -1.314e+05 1.47e+05 -0.892 0.372 -4.2e+05 1.57e+05
water_temp_4 salinity_4 3.94e+05 1.62e+05 2.435 0.015 7.69e+04 7.11e+05
water_temp_4 water_temp_6 -2336.5834 1077.528 -2.168 0.030 -4448.522 -224.645
water_temp_4 salinity_6 -2.735e+05 1.23e+05 -2.215 0.027 -5.15e+05 -3.15e+04
water_temp_4 water_temp_8 4886.1956 1706.400 2.863 0.004 1541.677 8230.714
water_temp_4 salinity_8 3.531e+04 2.9e+04 1.216 0.224 -2.16e+04 9.22e+04
salinity_4 water_temp_6 -4.262e+05 1.69e+05 -2.522 0.012 -7.57e+05 -9.5e+04
salinity_4 salinity_6 -1.17e+05 8.84e+04 -1.324 0.186 -2.9e+05 5.62e+04
salinity_4 water_temp_8 1.216e+05 6.33e+04 1.920 0.055 -2506.271 2.46e+05
salinity_4 salinity_8 1.384e+05 1.02e+05 1.363 0.173 -6.06e+04 3.37e+05
water_temp_6 salinity_6 2.52e+05 1.17e+05 2.155 0.031 2.28e+04 4.81e+05
water_temp_6 water_temp_8 -2008.3934 640.127 -3.137 0.002 -3263.033 -753.754
water_temp_6 salinity_8 -4.712e+04 2.42e+04 -1.948 0.051 -9.45e+04 279.613
salinity_6 water_temp_8 -4.939e+04 4.21e+04 -1.174 0.240 -1.32e+05 3.31e+04
salinity_6 salinity_8 -3.78e+04 3.87e+04 -0.976 0.329 -1.14e+05 3.81e+04
water_temp_8 salinity_8 1.248e+04 7149.376 1.746 0.081 -1530.566 2.65e+04
==============================================================================
Omnibus: 93894.503 Durbin-Watson: 2.000
Prob(Omnibus): 0.000 Jarque-Bera (JB): 1482125.420
Skew: -4.188 Prob(JB): 0.00
Kurtosis: 18.567 Cond. No. 6.36e+09
==============================================================================
Notes:
[1] R² is computed without centering (uncentered) since the model does not contain a constant.
[2] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[3] The condition number is large, 6.36e+09. This might indicate that there are
strong multicollinearity or other numerical problems.
fit_interaction_model(df, 'SST_C')
OLS Regression Results
=======================================================================================
Dep. Variable: y R-squared (uncentered): 0.011
Model: OLS Adj. R-squared (uncentered): 0.011
Method: Least Squares F-statistic: 23.55
Date: Tue, 15 Jun 2021 Prob (F-statistic): 2.84e-233
Time: 19:58:29 Log-Likelihood: -7.7592e+05
No. Observations: 113837 AIC: 1.552e+06
Df Residuals: 113782 BIC: 1.552e+06
Df Model: 55
Covariance Type: nonrobust
=============================================================================================
coef std err t P>|t| [0.025 0.975]
---------------------------------------------------------------------------------------------
water_temp_0 1397.1124 1804.293 0.774 0.439 -2139.274 4933.499
salinity_0 -4.48e+04 4.89e+04 -0.916 0.360 -1.41e+05 5.11e+04
water_temp_2 -5291.8586 7468.038 -0.709 0.479 -1.99e+04 9345.383
salinity_2 8.487e+04 1.13e+05 0.749 0.454 -1.37e+05 3.07e+05
water_temp_4 -6951.1520 1.89e+04 -0.368 0.713 -4.4e+04 3.01e+04
salinity_4 -3.082e+04 1.88e+05 -0.164 0.870 -4e+05 3.38e+05
water_temp_6 1.869e+04 1.94e+04 0.965 0.334 -1.93e+04 5.66e+04
salinity_6 -2.931e+04 1.6e+05 -0.183 0.855 -3.43e+05 2.84e+05
water_temp_8 -7828.4910 7273.288 -1.076 0.282 -2.21e+04 6427.043
salinity_8 2.005e+04 4.38e+04 0.458 0.647 -6.58e+04 1.06e+05
water_temp_0 salinity_0 1554.6673 4235.273 0.367 0.714 -6746.403 9855.738
water_temp_0 water_temp_2 401.2542 268.273 1.496 0.135 -124.557 927.066
water_temp_0 salinity_2 -1.191e+04 8537.874 -1.395 0.163 -2.86e+04 4825.382
water_temp_0 water_temp_4 -649.6158 1189.611 -0.546 0.585 -2981.235 1682.004
water_temp_0 salinity_4 2922.8431 1.97e+04 0.148 0.882 -3.57e+04 4.15e+04
water_temp_0 water_temp_6 -414.9752 1580.758 -0.263 0.793 -3513.238 2683.287
water_temp_0 salinity_6 1.451e+04 1.77e+04 0.822 0.411 -2.01e+04 4.91e+04
water_temp_0 water_temp_8 711.7556 638.555 1.115 0.265 -539.802 1963.313
water_temp_0 salinity_8 -7158.8773 4214.899 -1.698 0.089 -1.54e+04 1102.261
salinity_0 water_temp_2 -1.48e+04 2.19e+04 -0.677 0.499 -5.77e+04 2.81e+04
salinity_0 salinity_2 -1.704e+04 2.49e+04 -0.685 0.493 -6.58e+04 3.17e+04
salinity_0 water_temp_4 1.419e+05 6.8e+04 2.087 0.037 8663.150 2.75e+05
salinity_0 salinity_4 2.934e+05 2.48e+05 1.182 0.237 -1.93e+05 7.8e+05
salinity_0 water_temp_6 -2.03e+05 7.11e+04 -2.854 0.004 -3.42e+05 -6.36e+04
salinity_0 salinity_6 -3.064e+05 2.98e+05 -1.029 0.304 -8.9e+05 2.77e+05
salinity_0 water_temp_8 7.476e+04 2.5e+04 2.988 0.003 2.57e+04 1.24e+05
salinity_0 salinity_8 3.097e+04 9.36e+04 0.331 0.741 -1.52e+05 2.14e+05
water_temp_2 salinity_2 4.416e+04 3.95e+04 1.117 0.264 -3.33e+04 1.22e+05
water_temp_2 water_temp_4 -1482.2232 1191.850 -1.244 0.214 -3818.231 853.784
water_temp_2 salinity_4 -9.23e+04 6.15e+04 -1.500 0.134 -2.13e+05 2.83e+04
water_temp_2 water_temp_6 4416.9555 2539.029 1.740 0.082 -559.502 9393.413
water_temp_2 salinity_6 5.737e+04 5.32e+04 1.079 0.281 -4.69e+04 1.62e+05
water_temp_2 water_temp_8 -3524.3918 1499.116 -2.351 0.019 -6462.637 -586.146
water_temp_2 salinity_8 5862.1804 1.25e+04 0.469 0.639 -1.87e+04 3.04e+04
salinity_2 water_temp_4 -2.98e+05 1.25e+05 -2.383 0.017 -5.43e+05 -5.29e+04
salinity_2 salinity_4 -3.142e+05 2.44e+05 -1.285 0.199 -7.93e+05 1.65e+05
salinity_2 water_temp_6 4.242e+05 1.36e+05 3.123 0.002 1.58e+05 6.9e+05
salinity_2 salinity_6 4.612e+05 3.7e+05 1.246 0.213 -2.64e+05 1.19e+06
salinity_2 water_temp_8 -1.593e+05 5.04e+04 -3.164 0.002 -2.58e+05 -6.06e+04
salinity_2 salinity_8 -1.315e+05 1.47e+05 -0.893 0.372 -4.2e+05 1.57e+05
water_temp_4 salinity_4 3.942e+05 1.62e+05 2.436 0.015 7.71e+04 7.11e+05
water_temp_4 water_temp_6 -2340.9298 1077.553 -2.172 0.030 -4452.917 -228.942
water_temp_4 salinity_6 -2.735e+05 1.23e+05 -2.215 0.027 -5.16e+05 -3.15e+04
water_temp_4 water_temp_8 4891.4076 1706.440 2.866 0.004 1546.811 8236.004
water_temp_4 salinity_8 3.53e+04 2.9e+04 1.216 0.224 -2.16e+04 9.22e+04
salinity_4 water_temp_6 -4.263e+05 1.69e+05 -2.523 0.012 -7.58e+05 -9.51e+04
salinity_4 salinity_6 -1.17e+05 8.84e+04 -1.323 0.186 -2.9e+05 5.63e+04
salinity_4 water_temp_8 1.216e+05 6.33e+04 1.920 0.055 -2507.794 2.46e+05
salinity_4 salinity_8 1.384e+05 1.02e+05 1.363 0.173 -6.06e+04 3.37e+05
water_temp_6 salinity_6 2.521e+05 1.17e+05 2.155 0.031 2.28e+04 4.81e+05
water_temp_6 water_temp_8 -2009.1971 640.142 -3.139 0.002 -3263.866 -754.529
water_temp_6 salinity_8 -4.711e+04 2.42e+04 -1.948 0.051 -9.45e+04 285.210
salinity_6 water_temp_8 -4.939e+04 4.21e+04 -1.174 0.240 -1.32e+05 3.31e+04
salinity_6 salinity_8 -3.789e+04 3.87e+04 -0.978 0.328 -1.14e+05 3.81e+04
water_temp_8 salinity_8 1.249e+04 7149.542 1.747 0.081 -1523.475 2.65e+04
==============================================================================
Omnibus: 93894.534 Durbin-Watson: 2.000
Prob(Omnibus): 0.000 Jarque-Bera (JB): 1482127.690
Skew: -4.188 Prob(JB): 0.00
Kurtosis: 18.567 Cond. No. 6.36e+09
==============================================================================
Notes:
[1] R² is computed without centering (uncentered) since the model does not contain a constant.
[2] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[3] The condition number is large, 6.36e+09. This might indicate that there are
strong multicollinearity or other numerical problems.
fit_interaction_model(df, 'SAL_permil')
OLS Regression Results
=======================================================================================
Dep. Variable: y R-squared (uncentered): 0.005
Model: OLS Adj. R-squared (uncentered): 0.005
Method: Least Squares F-statistic: 11.08
Date: Tue, 15 Jun 2021 Prob (F-statistic): 3.10e-94
Time: 19:58:31 Log-Likelihood: -7.7684e+05
No. Observations: 113837 AIC: 1.554e+06
Df Residuals: 113782 BIC: 1.554e+06
Df Model: 55
Covariance Type: nonrobust
=============================================================================================
coef std err t P>|t| [0.025 0.975]
---------------------------------------------------------------------------------------------
water_temp_0 1367.5742 1818.942 0.752 0.452 -2197.524 4932.673
salinity_0 -4.587e+04 4.93e+04 -0.930 0.352 -1.43e+05 5.08e+04
water_temp_2 -5105.8680 7528.672 -0.678 0.498 -1.99e+04 9650.216
salinity_2 8.92e+04 1.14e+05 0.781 0.435 -1.35e+05 3.13e+05
water_temp_4 -6757.1157 1.91e+04 -0.355 0.723 -4.41e+04 3.06e+04
salinity_4 -3.557e+04 1.9e+05 -0.187 0.851 -4.08e+05 3.36e+05
water_temp_6 1.796e+04 1.95e+04 0.920 0.357 -2.03e+04 5.62e+04
salinity_6 -2.834e+04 1.61e+05 -0.176 0.860 -3.44e+05 2.88e+05
water_temp_8 -7458.0006 7332.341 -1.017 0.309 -2.18e+04 6913.276
salinity_8 2.057e+04 4.42e+04 0.466 0.641 -6.6e+04 1.07e+05
water_temp_0 salinity_0 1617.6373 4269.660 0.379 0.705 -6750.831 9986.105
water_temp_0 water_temp_2 401.2704 270.451 1.484 0.138 -128.810 931.351
water_temp_0 salinity_2 -1.202e+04 8607.195 -1.396 0.163 -2.89e+04 4852.843
water_temp_0 water_temp_4 -677.5743 1199.270 -0.565 0.572 -3028.125 1672.976
water_temp_0 salinity_4 2810.7528 1.99e+04 0.142 0.887 -3.61e+04 4.17e+04
water_temp_0 water_temp_6 -376.6868 1593.593 -0.236 0.813 -3500.105 2746.731
water_temp_0 salinity_6 1.461e+04 1.78e+04 0.820 0.412 -2.03e+04 4.95e+04
water_temp_0 water_temp_8 702.0970 643.739 1.091 0.275 -559.622 1963.816
water_temp_0 salinity_8 -7094.4059 4249.121 -1.670 0.095 -1.54e+04 1233.806
salinity_0 water_temp_2 -1.531e+04 2.21e+04 -0.694 0.488 -5.85e+04 2.79e+04
salinity_0 salinity_2 -1.787e+04 2.51e+04 -0.713 0.476 -6.7e+04 3.13e+04
salinity_0 water_temp_4 1.427e+05 6.85e+04 2.082 0.037 8364.997 2.77e+05
salinity_0 salinity_4 2.981e+05 2.5e+05 1.192 0.233 -1.92e+05 7.88e+05
salinity_0 water_temp_6 -2.034e+05 7.17e+04 -2.836 0.005 -3.44e+05 -6.28e+04
salinity_0 salinity_6 -3.108e+05 3e+05 -1.035 0.301 -8.99e+05 2.78e+05
salinity_0 water_temp_8 7.478e+04 2.52e+04 2.965 0.003 2.53e+04 1.24e+05
salinity_0 salinity_8 3.147e+04 9.43e+04 0.334 0.739 -1.53e+05 2.16e+05
water_temp_2 salinity_2 4.472e+04 3.98e+04 1.122 0.262 -3.34e+04 1.23e+05
water_temp_2 water_temp_4 -1451.4300 1201.527 -1.208 0.227 -3806.404 903.544
water_temp_2 salinity_4 -9.289e+04 6.2e+04 -1.497 0.134 -2.15e+05 2.87e+04
water_temp_2 water_temp_6 4369.6759 2559.643 1.707 0.088 -647.186 9386.538
water_temp_2 salinity_6 5.811e+04 5.36e+04 1.084 0.278 -4.7e+04 1.63e+05
water_temp_2 water_temp_8 -3509.7135 1511.288 -2.322 0.020 -6471.815 -547.612
water_temp_2 salinity_8 5651.7455 1.26e+04 0.448 0.654 -1.91e+04 3.04e+04
salinity_2 water_temp_4 -2.995e+05 1.26e+05 -2.375 0.018 -5.47e+05 -5.24e+04
salinity_2 salinity_4 -3.173e+05 2.46e+05 -1.287 0.198 -8e+05 1.66e+05
salinity_2 water_temp_6 4.261e+05 1.37e+05 3.112 0.002 1.58e+05 6.94e+05
salinity_2 salinity_6 4.665e+05 3.73e+05 1.250 0.211 -2.65e+05 1.2e+06
salinity_2 water_temp_8 -1.602e+05 5.08e+04 -3.156 0.002 -2.6e+05 -6.07e+04
salinity_2 salinity_8 -1.33e+05 1.48e+05 -0.896 0.370 -4.24e+05 1.58e+05
water_temp_4 salinity_4 3.971e+05 1.63e+05 2.435 0.015 7.74e+04 7.17e+05
water_temp_4 water_temp_6 -2334.6607 1086.302 -2.149 0.032 -4463.796 -205.526
water_temp_4 salinity_6 -2.762e+05 1.24e+05 -2.219 0.027 -5.2e+05 -3.22e+04
water_temp_4 water_temp_8 4883.5615 1720.295 2.839 0.005 1511.810 8255.313
water_temp_4 salinity_8 3.574e+04 2.93e+04 1.221 0.222 -2.16e+04 9.31e+04
salinity_4 water_temp_6 -4.301e+05 1.7e+05 -2.524 0.012 -7.64e+05 -9.61e+04
salinity_4 salinity_6 -1.186e+05 8.91e+04 -1.332 0.183 -2.93e+05 5.6e+04
salinity_4 water_temp_8 1.232e+05 6.39e+04 1.929 0.054 -1969.706 2.48e+05
salinity_4 salinity_8 1.386e+05 1.02e+05 1.354 0.176 -6.2e+04 3.39e+05
water_temp_6 salinity_6 2.547e+05 1.18e+05 2.161 0.031 2.37e+04 4.86e+05
water_temp_6 water_temp_8 -2006.5061 645.339 -3.109 0.002 -3271.361 -741.651
water_temp_6 salinity_8 -4.754e+04 2.44e+04 -1.950 0.051 -9.53e+04 243.333
salinity_6 water_temp_8 -5.023e+04 4.24e+04 -1.184 0.236 -1.33e+05 3.29e+04
salinity_6 salinity_8 -3.715e+04 3.91e+04 -0.951 0.342 -1.14e+05 3.94e+04
water_temp_8 salinity_8 1.262e+04 7207.590 1.750 0.080 -1509.937 2.67e+04
==============================================================================
Omnibus: 93894.905 Durbin-Watson: 2.000
Prob(Omnibus): 0.000 Jarque-Bera (JB): 1482147.211
Skew: -4.188 Prob(JB): 0.00
Kurtosis: 18.567 Cond. No. 6.36e+09
==============================================================================
Notes:
[1] R² is computed without centering (uncentered) since the model does not contain a constant.
[2] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[3] The condition number is large, 6.36e+09. This might indicate that there are
strong multicollinearity or other numerical problems.
fit_interaction_model(df, 'fCO2_SW@SST_uatm')
OLS Regression Results
=======================================================================================
Dep. Variable: y R-squared (uncentered): 0.551
Model: OLS Adj. R-squared (uncentered): 0.550
Method: Least Squares F-statistic: 2536.
Date: Tue, 15 Jun 2021 Prob (F-statistic): 0.00
Time: 19:58:32 Log-Likelihood: -8.1121e+05
No. Observations: 113837 AIC: 1.623e+06
Df Residuals: 113782 BIC: 1.623e+06
Df Model: 55
Covariance Type: nonrobust
=============================================================================================
coef std err t P>|t| [0.025 0.975]
---------------------------------------------------------------------------------------------
water_temp_0 2212.4589 2460.113 0.899 0.368 -2609.326 7034.244
salinity_0 -6.252e+04 6.67e+04 -0.938 0.348 -1.93e+05 6.82e+04
water_temp_2 -5815.2583 1.02e+04 -0.571 0.568 -2.58e+04 1.41e+04
salinity_2 9.144e+04 1.54e+05 0.592 0.554 -2.11e+05 3.94e+05
water_temp_4 -1.784e+04 2.58e+04 -0.692 0.489 -6.83e+04 3.27e+04
salinity_4 -2.075e+04 2.57e+05 -0.081 0.936 -5.24e+05 4.82e+05
water_temp_6 3.435e+04 2.64e+04 1.301 0.193 -1.74e+04 8.61e+04
salinity_6 -3.303e+04 2.18e+05 -0.151 0.880 -4.61e+05 3.94e+05
water_temp_8 -1.297e+04 9916.968 -1.308 0.191 -3.24e+04 6470.313
salinity_8 2.489e+04 5.97e+04 0.417 0.677 -9.22e+04 1.42e+05
water_temp_0 salinity_0 1165.8460 5774.701 0.202 0.840 -1.02e+04 1.25e+04
water_temp_0 water_temp_2 654.7521 365.785 1.790 0.073 -62.180 1371.685
water_temp_0 salinity_2 -1.595e+04 1.16e+04 -1.370 0.171 -3.88e+04 6863.885
water_temp_0 water_temp_4 -1571.2084 1622.008 -0.969 0.333 -4750.320 1607.904
water_temp_0 salinity_4 3062.3239 2.68e+04 0.114 0.909 -4.96e+04 5.57e+04
water_temp_0 water_temp_6 318.6669 2155.329 0.148 0.882 -3905.746 4543.080
water_temp_0 salinity_6 2.142e+04 2.41e+04 0.889 0.374 -2.58e+04 6.86e+04
water_temp_0 water_temp_8 662.5184 870.655 0.761 0.447 -1043.952 2368.989
water_temp_0 salinity_8 -9804.9629 5746.922 -1.706 0.088 -2.11e+04 1458.918
salinity_0 water_temp_2 -1.795e+04 2.98e+04 -0.602 0.547 -7.64e+04 4.05e+04
salinity_0 salinity_2 -2.877e+04 3.39e+04 -0.848 0.396 -9.52e+04 3.77e+04
salinity_0 water_temp_4 1.895e+05 9.27e+04 2.044 0.041 7760.694 3.71e+05
salinity_0 salinity_4 4.353e+05 3.38e+05 1.286 0.198 -2.28e+05 1.1e+06
salinity_0 water_temp_6 -2.662e+05 9.7e+04 -2.745 0.006 -4.56e+05 -7.61e+04
salinity_0 salinity_6 -4.36e+05 4.06e+05 -1.074 0.283 -1.23e+06 3.6e+05
salinity_0 water_temp_8 9.415e+04 3.41e+04 2.760 0.006 2.73e+04 1.61e+05
salinity_0 salinity_8 3.081e+04 1.28e+05 0.241 0.809 -2.19e+05 2.81e+05
water_temp_2 salinity_2 5.71e+04 5.39e+04 1.059 0.289 -4.85e+04 1.63e+05
water_temp_2 water_temp_4 -1725.3101 1625.061 -1.062 0.288 -4910.405 1459.785
water_temp_2 salinity_4 -1.226e+05 8.39e+04 -1.461 0.144 -2.87e+05 4.19e+04
water_temp_2 water_temp_6 5292.1131 3461.909 1.529 0.126 -1493.177 1.21e+04
water_temp_2 salinity_6 7.466e+04 7.25e+04 1.029 0.303 -6.75e+04 2.17e+05
water_temp_2 water_temp_8 -4479.1201 2044.012 -2.191 0.028 -8485.353 -472.887
water_temp_2 salinity_8 9174.7654 1.71e+04 0.538 0.591 -2.43e+04 4.26e+04
salinity_2 water_temp_4 -3.986e+05 1.71e+05 -2.337 0.019 -7.33e+05 -6.44e+04
salinity_2 salinity_4 -4.643e+05 3.33e+05 -1.393 0.164 -1.12e+06 1.89e+05
salinity_2 water_temp_6 5.613e+05 1.85e+05 3.031 0.002 1.98e+05 9.24e+05
salinity_2 salinity_6 6.602e+05 5.05e+05 1.308 0.191 -3.29e+05 1.65e+06
salinity_2 water_temp_8 -2.05e+05 6.87e+04 -2.986 0.003 -3.4e+05 -7.04e+04
salinity_2 salinity_8 -1.687e+05 2.01e+05 -0.840 0.401 -5.62e+05 2.25e+05
water_temp_4 salinity_4 5.363e+05 2.21e+05 2.431 0.015 1.04e+05 9.69e+05
water_temp_4 water_temp_6 -3086.4830 1469.220 -2.101 0.036 -5966.132 -206.835
water_temp_4 salinity_6 -3.729e+05 1.68e+05 -2.215 0.027 -7.03e+05 -4.29e+04
water_temp_4 water_temp_8 7014.3330 2326.693 3.015 0.003 2454.050 1.16e+04
water_temp_4 salinity_8 4.576e+04 3.96e+04 1.156 0.248 -3.18e+04 1.23e+05
salinity_4 water_temp_6 -5.841e+05 2.3e+05 -2.535 0.011 -1.04e+06 -1.32e+05
salinity_4 salinity_6 -1.664e+05 1.21e+05 -1.380 0.167 -4.03e+05 6.98e+04
salinity_4 water_temp_8 1.678e+05 8.64e+04 1.943 0.052 -1505.552 3.37e+05
salinity_4 salinity_8 1.955e+05 1.38e+05 1.412 0.158 -7.58e+04 4.67e+05
water_temp_6 salinity_6 3.524e+05 1.59e+05 2.210 0.027 3.99e+04 6.65e+05
water_temp_6 water_temp_8 -3079.5403 872.820 -3.528 0.000 -4790.253 -1368.827
water_temp_6 salinity_8 -6.394e+04 3.3e+04 -1.939 0.052 -1.29e+05 687.747
salinity_6 water_temp_8 -7.472e+04 5.74e+04 -1.302 0.193 -1.87e+05 3.77e+04
salinity_6 salinity_8 -5.775e+04 5.28e+04 -1.093 0.274 -1.61e+05 4.58e+04
water_temp_8 salinity_8 1.808e+04 9748.243 1.855 0.064 -1028.087 3.72e+04
==============================================================================
Omnibus: 93825.981 Durbin-Watson: 1.999
Prob(Omnibus): 0.000 Jarque-Bera (JB): 1479200.544
Skew: -4.184 Prob(JB): 0.00
Kurtosis: 18.551 Cond. No. 6.36e+09
==============================================================================
Notes:
[1] R² is computed without centering (uncentered) since the model does not contain a constant.
[2] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[3] The condition number is large, 6.36e+09. This might indicate that there are
strong multicollinearity or other numerical problems.
fit_interaction_model(df, 'fCO2_ATM_interpolated_uatm')
OLS Regression Results
=======================================================================================
Dep. Variable: y R-squared (uncentered): 0.550
Model: OLS Adj. R-squared (uncentered): 0.550
Method: Least Squares F-statistic: 2529.
Date: Tue, 15 Jun 2021 Prob (F-statistic): 0.00
Time: 19:58:34 Log-Likelihood: -8.1119e+05
No. Observations: 113837 AIC: 1.622e+06
Df Residuals: 113782 BIC: 1.623e+06
Df Model: 55
Covariance Type: nonrobust
=============================================================================================
coef std err t P>|t| [0.025 0.975]
---------------------------------------------------------------------------------------------
water_temp_0 2112.8658 2459.590 0.859 0.390 -2707.892 6933.624
salinity_0 -5.038e+04 6.67e+04 -0.756 0.450 -1.81e+05 8.03e+04
water_temp_2 -8036.4936 1.02e+04 -0.789 0.430 -2.8e+04 1.19e+04
salinity_2 1.115e+05 1.54e+05 0.722 0.471 -1.91e+05 4.14e+05
water_temp_4 -1.029e+04 2.58e+04 -0.399 0.690 -6.08e+04 4.02e+04
salinity_4 -5.187e+04 2.57e+05 -0.202 0.840 -5.55e+05 4.51e+05
water_temp_6 2.636e+04 2.64e+04 0.999 0.318 -2.54e+04 7.81e+04
salinity_6 -4.5e+04 2.18e+05 -0.206 0.837 -4.72e+05 3.82e+05
water_temp_8 -1.016e+04 9914.856 -1.025 0.306 -2.96e+04 9274.128
salinity_8 3.581e+04 5.97e+04 0.600 0.549 -8.12e+04 1.53e+05
water_temp_0 salinity_0 1642.6484 5773.472 0.285 0.776 -9673.269 1.3e+04
water_temp_0 water_temp_2 576.2747 365.707 1.576 0.115 -140.505 1293.055
water_temp_0 salinity_2 -1.547e+04 1.16e+04 -1.329 0.184 -3.83e+04 7342.816
water_temp_0 water_temp_4 -634.2707 1621.663 -0.391 0.696 -3812.706 2544.164
water_temp_0 salinity_4 3850.4720 2.68e+04 0.143 0.886 -4.88e+04 5.65e+04
water_temp_0 water_temp_6 -1002.1520 2154.870 -0.465 0.642 -5225.665 3221.361
water_temp_0 salinity_6 1.957e+04 2.41e+04 0.813 0.416 -2.76e+04 6.68e+04
water_temp_0 water_temp_8 1126.2526 870.470 1.294 0.196 -579.855 2832.360
water_temp_0 salinity_8 -9710.1713 5745.699 -1.690 0.091 -2.1e+04 1551.311
salinity_0 water_temp_2 -1.972e+04 2.98e+04 -0.661 0.508 -7.82e+04 3.87e+04
salinity_0 salinity_2 -2.409e+04 3.39e+04 -0.710 0.477 -9.05e+04 4.24e+04
salinity_0 water_temp_4 1.944e+05 9.27e+04 2.097 0.036 1.27e+04 3.76e+05
salinity_0 salinity_4 4.017e+05 3.38e+05 1.188 0.235 -2.61e+05 1.06e+06
salinity_0 water_temp_6 -2.795e+05 9.7e+04 -2.883 0.004 -4.7e+05 -8.95e+04
salinity_0 salinity_6 -4.147e+05 4.06e+05 -1.021 0.307 -1.21e+06 3.81e+05
salinity_0 water_temp_8 1.037e+05 3.41e+04 3.040 0.002 3.69e+04 1.71e+05
salinity_0 salinity_8 3.805e+04 1.28e+05 0.298 0.766 -2.12e+05 2.88e+05
water_temp_2 salinity_2 5.696e+04 5.39e+04 1.057 0.290 -4.87e+04 1.63e+05
water_temp_2 water_temp_4 -2323.8473 1624.715 -1.430 0.153 -5508.264 860.569
water_temp_2 salinity_4 -1.199e+05 8.39e+04 -1.429 0.153 -2.84e+05 4.45e+04
water_temp_2 water_temp_6 6358.1298 3461.172 1.837 0.066 -425.716 1.31e+04
water_temp_2 salinity_6 7.407e+04 7.25e+04 1.022 0.307 -6.8e+04 2.16e+05
water_temp_2 water_temp_8 -4858.7974 2043.577 -2.378 0.017 -8864.178 -853.417
water_temp_2 salinity_8 8993.9181 1.71e+04 0.527 0.598 -2.44e+04 4.24e+04
salinity_2 water_temp_4 -3.993e+05 1.71e+05 -2.342 0.019 -7.33e+05 -6.51e+04
salinity_2 salinity_4 -4.316e+05 3.33e+05 -1.295 0.195 -1.08e+06 2.22e+05
salinity_2 water_temp_6 5.785e+05 1.85e+05 3.124 0.002 2.16e+05 9.41e+05
salinity_2 salinity_6 6.306e+05 5.05e+05 1.249 0.211 -3.59e+05 1.62e+06
salinity_2 water_temp_8 -2.221e+05 6.86e+04 -3.235 0.001 -3.57e+05 -8.75e+04
salinity_2 salinity_8 -1.769e+05 2.01e+05 -0.881 0.378 -5.7e+05 2.17e+05
water_temp_4 salinity_4 5.172e+05 2.21e+05 2.345 0.019 8.49e+04 9.5e+05
water_temp_4 water_temp_6 -3063.0230 1468.907 -2.085 0.037 -5942.058 -183.988
water_temp_4 salinity_6 -3.597e+05 1.68e+05 -2.137 0.033 -6.9e+05 -2.98e+04
water_temp_4 water_temp_8 6592.5155 2326.198 2.834 0.005 2033.203 1.12e+04
water_temp_4 salinity_8 4.717e+04 3.96e+04 1.192 0.233 -3.04e+04 1.25e+05
salinity_4 water_temp_6 -5.66e+05 2.3e+05 -2.457 0.014 -1.02e+06 -1.14e+05
salinity_4 salinity_6 -1.617e+05 1.2e+05 -1.342 0.179 -3.98e+05 7.44e+04
salinity_4 water_temp_8 1.652e+05 8.63e+04 1.914 0.056 -4000.744 3.34e+05
salinity_4 salinity_8 1.926e+05 1.38e+05 1.391 0.164 -7.87e+04 4.64e+05
water_temp_6 salinity_6 3.298e+05 1.59e+05 2.069 0.039 1.73e+04 6.42e+05
water_temp_6 water_temp_8 -2771.1658 872.634 -3.176 0.001 -4481.515 -1060.817
water_temp_6 salinity_8 -6.316e+04 3.3e+04 -1.916 0.055 -1.28e+05 1449.655
salinity_6 water_temp_8 -6.248e+04 5.74e+04 -1.089 0.276 -1.75e+05 4.99e+04
salinity_6 salinity_8 -5.406e+04 5.28e+04 -1.024 0.306 -1.58e+05 4.95e+04
water_temp_8 salinity_8 1.586e+04 9746.168 1.627 0.104 -3243.654 3.5e+04
==============================================================================
Omnibus: 93857.225 Durbin-Watson: 1.999
Prob(Omnibus): 0.000 Jarque-Bera (JB): 1480208.951
Skew: -4.186 Prob(JB): 0.00
Kurtosis: 18.556 Cond. No. 6.36e+09
==============================================================================
Notes:
[1] R² is computed without centering (uncentered) since the model does not contain a constant.
[2] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[3] The condition number is large, 6.36e+09. This might indicate that there are
strong multicollinearity or other numerical problems.
fit_interaction_model(df, 'dfCO2_uatm')
OLS Regression Results
=======================================================================================
Dep. Variable: y R-squared (uncentered): 0.058
Model: OLS Adj. R-squared (uncentered): 0.057
Method: Least Squares F-statistic: 127.0
Date: Tue, 15 Jun 2021 Prob (F-statistic): 0.00
Time: 19:58:35 Log-Likelihood: -7.7291e+05
No. Observations: 113837 AIC: 1.546e+06
Df Residuals: 113782 BIC: 1.546e+06
Df Model: 55
Covariance Type: nonrobust
=============================================================================================
coef std err t P>|t| [0.025 0.975]
---------------------------------------------------------------------------------------------
water_temp_0 1450.2732 1757.189 0.825 0.409 -1993.792 4894.338
salinity_0 -5.569e+04 4.76e+04 -1.169 0.242 -1.49e+05 3.77e+04
water_temp_2 -2863.8993 7273.076 -0.394 0.694 -1.71e+04 1.14e+04
salinity_2 6.325e+04 1.1e+05 0.573 0.566 -1.53e+05 2.8e+05
water_temp_4 -1.416e+04 1.84e+04 -0.769 0.442 -5.02e+04 2.19e+04
salinity_4 -350.4962 1.83e+05 -0.002 0.998 -3.6e+05 3.59e+05
water_temp_6 2.586e+04 1.89e+04 1.371 0.170 -1.11e+04 6.28e+04
salinity_6 -1.581e+04 1.56e+05 -0.102 0.919 -3.21e+05 2.9e+05
water_temp_8 -1.032e+04 7083.410 -1.457 0.145 -2.42e+04 3559.641
salinity_8 8604.7319 4.27e+04 0.202 0.840 -7.5e+04 9.22e+04
water_temp_0 salinity_0 1078.0125 4124.706 0.261 0.794 -7006.349 9162.374
water_temp_0 water_temp_2 468.8477 261.270 1.794 0.073 -43.237 980.932
water_temp_0 salinity_2 -1.21e+04 8314.983 -1.456 0.145 -2.84e+04 4193.362
water_temp_0 water_temp_4 -1577.1470 1158.555 -1.361 0.173 -3847.897 693.603
water_temp_0 salinity_4 1977.1643 1.92e+04 0.103 0.918 -3.56e+04 3.96e+04
water_temp_0 water_temp_6 927.4705 1539.491 0.602 0.547 -2089.908 3944.849
water_temp_0 salinity_6 1.599e+04 1.72e+04 0.929 0.353 -1.77e+04 4.97e+04
water_temp_0 water_temp_8 226.7103 621.884 0.365 0.715 -992.173 1445.594
water_temp_0 salinity_8 -7014.7573 4104.864 -1.709 0.087 -1.51e+04 1030.714
salinity_0 water_temp_2 -1.294e+04 2.13e+04 -0.607 0.544 -5.47e+04 2.88e+04
salinity_0 salinity_2 -2.149e+04 2.42e+04 -0.887 0.375 -6.9e+04 2.6e+04
salinity_0 water_temp_4 1.335e+05 6.62e+04 2.015 0.044 3662.969 2.63e+05
salinity_0 salinity_4 3.186e+05 2.42e+05 1.318 0.187 -1.55e+05 7.92e+05
salinity_0 water_temp_6 -1.843e+05 6.93e+04 -2.660 0.008 -3.2e+05 -4.85e+04
salinity_0 salinity_6 -3.19e+05 2.9e+05 -1.100 0.272 -8.88e+05 2.5e+05
salinity_0 water_temp_8 6.316e+04 2.44e+04 2.592 0.010 1.54e+04 1.11e+05
salinity_0 salinity_8 2.301e+04 9.11e+04 0.253 0.801 -1.56e+05 2.02e+05
water_temp_2 salinity_2 4.339e+04 3.85e+04 1.127 0.260 -3.21e+04 1.19e+05
water_temp_2 water_temp_4 -827.9033 1160.735 -0.713 0.476 -3102.926 1447.120
water_temp_2 salinity_4 -9.226e+04 5.99e+04 -1.539 0.124 -2.1e+05 2.52e+04
water_temp_2 water_temp_6 3203.3217 2472.744 1.295 0.195 -1643.219 8049.863
water_temp_2 salinity_6 5.623e+04 5.18e+04 1.085 0.278 -4.53e+04 1.58e+05
water_temp_2 water_temp_8 -3036.7200 1459.980 -2.080 0.038 -5898.259 -175.181
water_temp_2 salinity_8 5810.8084 1.22e+04 0.477 0.633 -1.81e+04 2.97e+04
salinity_2 water_temp_4 -2.896e+05 1.22e+05 -2.378 0.017 -5.28e+05 -5.09e+04
salinity_2 salinity_4 -3.372e+05 2.38e+05 -1.416 0.157 -8.04e+05 1.3e+05
salinity_2 water_temp_6 3.958e+05 1.32e+05 2.992 0.003 1.37e+05 6.55e+05
salinity_2 salinity_6 4.776e+05 3.61e+05 1.325 0.185 -2.29e+05 1.18e+06
salinity_2 water_temp_8 -1.382e+05 4.9e+04 -2.817 0.005 -2.34e+05 -4.2e+04
salinity_2 salinity_8 -1.201e+05 1.43e+05 -0.837 0.403 -4.01e+05 1.61e+05
water_temp_4 salinity_4 4.021e+05 1.58e+05 2.552 0.011 9.32e+04 7.11e+05
water_temp_4 water_temp_6 -2290.3829 1049.422 -2.183 0.029 -4347.234 -233.531
water_temp_4 salinity_6 -2.787e+05 1.2e+05 -2.318 0.020 -5.14e+05 -4.3e+04
water_temp_4 water_temp_8 5160.1883 1661.891 3.105 0.002 1902.907 8417.470
water_temp_4 salinity_8 3.288e+04 2.83e+04 1.163 0.245 -2.25e+04 8.83e+04
salinity_4 water_temp_6 -4.328e+05 1.65e+05 -2.630 0.009 -7.55e+05 -1.1e+05
salinity_4 salinity_6 -1.188e+05 8.61e+04 -1.380 0.168 -2.87e+05 4.99e+04
salinity_4 water_temp_8 1.211e+05 6.17e+04 1.963 0.050 214.063 2.42e+05
salinity_4 salinity_8 1.372e+05 9.89e+04 1.387 0.165 -5.66e+04 3.31e+05
water_temp_6 salinity_6 2.674e+05 1.14e+05 2.348 0.019 4.41e+04 4.91e+05
water_temp_6 water_temp_8 -2253.5502 623.430 -3.615 0.000 -3475.464 -1031.636
water_temp_6 salinity_8 -4.649e+04 2.36e+04 -1.974 0.048 -9.26e+04 -329.887
salinity_6 water_temp_8 -6.024e+04 4.1e+04 -1.470 0.142 -1.41e+05 2.01e+04
salinity_6 salinity_8 -4e+04 3.77e+04 -1.060 0.289 -1.14e+05 3.4e+04
water_temp_8 salinity_8 1.433e+04 6962.895 2.058 0.040 679.621 2.8e+04
==============================================================================
Omnibus: 93725.391 Durbin-Watson: 2.000
Prob(Omnibus): 0.000 Jarque-Bera (JB): 1475107.402
Skew: -4.178 Prob(JB): 0.00
Kurtosis: 18.530 Cond. No. 6.36e+09
==============================================================================
Notes:
[1] R² is computed without centering (uncentered) since the model does not contain a constant.
[2] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[3] The condition number is large, 6.36e+09. This might indicate that there are
strong multicollinearity or other numerical problems.
import xgboost as xgb
import matplotlib.pyplot as plt
params = {
'max_depth': 4,
'max_leaves': 2**8,
'tree_method': 'gpu_hist',
'objective': 'reg:squarederror',
'grow_policy': 'lossguide',
'eval_metric': 'logloss',
'subsample': '0.8'
}
def fit_interaction_model(df, pred_col, n_interaction=2):
df = df.dropna()
X = df[X_col_names]
y = df[[pred_col]]
poly_features = PolynomialFeatures(n_interaction, interaction_only=True, include_bias=False)
X_inter = poly_features.fit_transform(X.as_gpu_matrix())
X_df = cudf.DataFrame(X_inter, columns=poly_features.get_feature_names(X.columns))
dtrain = xgb.DMatrix(X_df, y)
model = xgb.train(params, dtrain, num_boost_round=100)
scores = dict(sorted(model.get_score(importance_type='gain').items(), key=lambda item: item[1], reverse=True))
scores = pd.DataFrame.from_dict(scores, orient='index').reset_index()
scores.columns = ['interaction', 'F-score']
return scores
fit_interaction_model(df, 'xCO2_EQU_ppm')
| interaction | F-score | |
|---|---|---|
| 0 | salinity_4 water_temp_6 | 4.430559e+06 |
| 1 | water_temp_4 salinity_6 | 3.796217e+06 |
| 2 | salinity_0 water_temp_2 | 2.795584e+06 |
| 3 | water_temp_2 salinity_8 | 2.777022e+06 |
| 4 | salinity_0 water_temp_4 | 2.664439e+06 |
| 5 | salinity_4 | 2.586490e+06 |
| 6 | salinity_6 water_temp_8 | 2.442660e+06 |
| 7 | water_temp_4 | 2.351526e+06 |
| 8 | water_temp_4 salinity_4 | 2.331590e+06 |
| 9 | salinity_2 | 2.326387e+06 |
| 10 | water_temp_0 salinity_6 | 2.146548e+06 |
| 11 | water_temp_6 salinity_6 | 2.128905e+06 |
| 12 | water_temp_4 water_temp_8 | 2.027545e+06 |
| 13 | water_temp_2 salinity_4 | 1.974119e+06 |
| 14 | water_temp_0 water_temp_6 | 1.959638e+06 |
| 15 | water_temp_0 salinity_0 | 1.939111e+06 |
| 16 | salinity_0 salinity_8 | 1.904266e+06 |
| 17 | water_temp_2 salinity_6 | 1.900974e+06 |
| 18 | water_temp_2 | 1.889223e+06 |
| 19 | salinity_4 salinity_6 | 1.842115e+06 |
| 20 | water_temp_2 salinity_2 | 1.831252e+06 |
| 21 | water_temp_0 water_temp_8 | 1.813927e+06 |
| 22 | salinity_0 water_temp_8 | 1.809904e+06 |
| 23 | water_temp_2 water_temp_8 | 1.804140e+06 |
| 24 | water_temp_0 water_temp_4 | 1.791293e+06 |
| 25 | water_temp_2 water_temp_6 | 1.768099e+06 |
| 26 | salinity_0 salinity_4 | 1.760418e+06 |
| 27 | water_temp_0 water_temp_2 | 1.743686e+06 |
| 28 | salinity_0 salinity_6 | 1.733822e+06 |
| 29 | salinity_0 | 1.721878e+06 |
| 30 | salinity_2 water_temp_6 | 1.697035e+06 |
| 31 | water_temp_4 water_temp_6 | 1.664098e+06 |
| 32 | water_temp_0 | 1.654031e+06 |
| 33 | salinity_2 salinity_4 | 1.650368e+06 |
| 34 | water_temp_0 salinity_2 | 1.637497e+06 |
| 35 | salinity_4 salinity_8 | 1.601531e+06 |
| 36 | salinity_2 water_temp_4 | 1.593254e+06 |
| 37 | water_temp_8 salinity_8 | 1.584930e+06 |
| 38 | water_temp_6 water_temp_8 | 1.463999e+06 |
| 39 | salinity_2 water_temp_8 | 1.455252e+06 |
| 40 | salinity_6 salinity_8 | 1.451010e+06 |
| 41 | salinity_6 | 1.399099e+06 |
| 42 | salinity_8 | 1.385359e+06 |
| 43 | water_temp_6 salinity_8 | 1.384313e+06 |
| 44 | water_temp_0 salinity_8 | 1.363816e+06 |
| 45 | water_temp_8 | 1.350263e+06 |
| 46 | salinity_0 salinity_2 | 1.342739e+06 |
| 47 | salinity_4 water_temp_8 | 1.282066e+06 |
| 48 | salinity_0 water_temp_6 | 1.267655e+06 |
| 49 | water_temp_6 | 1.216087e+06 |
| 50 | water_temp_0 salinity_4 | 1.138838e+06 |
| 51 | water_temp_4 salinity_8 | 1.137954e+06 |
| 52 | salinity_2 salinity_8 | 1.067442e+06 |
| 53 | water_temp_2 water_temp_4 | 9.797247e+05 |
| 54 | salinity_2 salinity_6 | 7.626201e+05 |